A Novel Blind Source Separation Method Based on the Extended Natural Gradient

In this paper, a new method is introduced to derive the extended natural gradient, which was proposed by Lewicki and Sejnowski in [1]. However, they made their derivation under many approximations, and the proof is also very complicated. To give a more rigors mathematical proof for this gradient, the Lie group invariance property is introduced which makes the proof much easier and straightforward. In addition, an iterative algorithm through Newton's method is also given to estimate the sources efficiently. The results of the experiments confirm the efficiency of the proposed method.